JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B12, 2380, doi:10.1029/2001JB000713, 2002
Joint inversion of normal mode and body wave data for inner core anisotropy 2. Possible complexities Miaki Ishii and Adam M. Dziewon´ski Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA
Jeroen Tromp Seismological Laboratory, California Institute of Technology, Pasadena, California, USA
Go¨ran Ekstro¨m Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA Received 19 June 2001; revised 10 June 2002; accepted 8 July 2002; published 31 December 2002.
[1] In this study we focus on inner core sensitive body wave data to investigate lateral and radial heterogeneity within the inner core. Normal mode data are used to constrain a global model and to monitor if complexities introduced by body wave data are compatible with mode measurements. In particular, we investigate the possibilities of an isotropic layer near the inner core boundary and large-scale variations in anisotropy such as hemispheric dependence proposed in studies based upon differential travel time data. Travel time data from distances between 130 and 140 require anisotropy near the inner core boundary. This evidence is supported by differential travel time data based upon diffracted waves, contrasting the previous inferences of isotropy at the surface of the inner core. Our experiments also show that variations at a hemispheric scale are not necessary and that the sources of apparent hemispheric differences can be localized. A comparison of differential and absolute travel time data suggests that differences in inferred inner core anisotropy models arise mainly from a few anomalous paths. These paths are responsible for the strong anisotropy which is characteristic of models based upon differential data. Assuming constant anisotropy in the inner core, we investigate the distribution of residual differential travel times at the entry and exit points of rays turning within the outer core. The results are consistent with existing models of structure near the core-mantle boundary. Placing the source of the difference between differential and absolute travel time data in the lowermost mantle gives a more satisfactory result than attempting to model it with a complex inner core. INDEX TERMS: 7207 Seismology: Core and mantle; 7260 Seismology: Theory and modeling; 7203 Seismology: Body wave propagation; 7255 Seismology: Surface waves and free oscillations; KEYWORDS: inner core, anisotropy, PKIKP, differential travel times, hemispheric variations
Citation: Ishii, M., A. M. Dziewon´ski, J. Tromp, and G. Ekstro¨m, Joint inversion of normal mode and body wave data for inner core anisotropy, 2, Possible complexities, J. Geophys. Res., 107(B12), 2380, doi:10.1029/2001JB000713, 2002.
1. Introduction differential travel time data is the similarity of the mantle ray path of waves turning in the outer core (BC or AB) and the [2] The properties of the Earth’s inner core have been inner core (DF) (Figure 1). This similarity allows one to investigated using three different types of data: normal modes assume that differential measurements do not include effects [e.g., Woodhouse et al., 1986; Tromp,1993;Durek and due to the source, receiver, or mantle, and hence that the Romanowicz, 1999], absolute travel times of PKIKP (or travel time anomalies are solely due to the path within the PKP ) [e.g., Morelli et al., 1986; Shearer et al., 1988; DF inner core. Many models of the inner core have been Su and Dziewon´ski, 1995], and the differential travel proposed using differential travel time data, some of which times BC DF (or PKP PKP )andAB DF (or BC DF contain structures not seen in models based upon other types PKP PKP ) [e.g., Creager, 1992; Song and Helmberger, AB DF of data, such as an isotropic layer near the inner core 1993; Vinnik et al., 1994; McSweeney et al., 1997; Tanaka boundary [e.g., Song and Helmberger, 1998], a transition and Hamaguchi, 1997]. The advantage of the high-quality zone within the inner core [e.g., Song and Helmberger, 1998], and hemispherically dependent anisotropy [e.g., Copyright 2002 by the American Geophysical Union. Tanaka and Hamaguchi, 1997; Creager, 1999; Niu and 0148-0227/02/2001JB000713$09.00 Wen, 2001].
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Figure 1. (left) Ray paths for AB, BC, and DF at an epicentral distance range of 150 , and (right) a travel time table for PKP branch using PREM [Dziewon´ski and Anderson, 1981]. For the travel time table we use an earthquake with a source depth of 300 km.
[3] In the companion paper (Ishii et al. [2002], hereinafter Vinnik et al., 1994; Song, 1996; McSweeney et al., 1997], referred to as paper 1), we demonstrate that it is relatively whereas absolute travel times tend to result in models with easy to obtain a simple anisotropic inner core model which weaker anisotropy [e.g., Su and Dziewon´ski, 1995]. To fits all three types of data. Normal mode and mantle- investigate this discrepancy, we compare absolute and corrected DF data are compatible with one another and differential travel time data. Contamination of differential good fits can be achieved using a constant anisotropy data due to mantle structure near the core-mantle boundary model. Differential travel time data are harder to fit. In this (CMB) has also been suggested [e.g., Breger et al., 1999, paper we explore the source of this difficulty by (1) 2000], especially for the AB rays. We follow this suggestion considering in detail paths sampled by differential data; and investigate if the residual differential travel time signal (2) introducing structure within the inner core; and (3) based upon a constant anisotropy model can be placed in the investigating the possible effects of D" heterogeneity. Our mantle. focus is on large-scale structure, and therefore the existence of lateral variations [e.g., Su and Dziewon´ski, 1995], except for hemispheric variations or small-scale structure [e.g., 2. Comparison of Body Wave Data Creager, 1997; Dziewon´ski, 2000; Vidale and Earle, [6] We use normal mode splitting functions [He and 2000], is addressed only briefly. We assume that the Tromp, 1996; Resovsky and Ritzwoller, 1998; Durek and symmetry axis of the inner core is aligned with the rotation Romanowicz, 1999], ISC DF residuals, and high-quality axis, and we do not consider differential rotation [e.g., differential travel time data [Creager, 1992; Vinnik et al., Shearer and Toy, 1991; Creager, 1992; Song and Richards, 1994; McSweeney, 1995; Song, 1996; Creager, 1997; 1996; Su et al., 1996; Souriau and Poupinet, 2000] in our McSweeney et al., 1997; Tanaka and Hamaguchi, 1997; analysis. A detailed discussion of the theory, data, and Creager, 1999] to investigate the structure of the inner core. inversion method used in this paper can be found in paper 1. Before using these data, we explore the differences between [4] Using all available data, we investigate if the intro- mantle-corrected absolute and differential travel time data. duction of an isotropic layer near the inner core boundary For details of data processing, see paper 1. If the mantle (ICB) can improve the fit, especially to differential travel correction to absolute and differential travel times is appro- time data [e.g., Song and Helmberger, 1995; Creager, priate, these two sets of data should agree well. The fact that 2000]. We also explore the possibility of hemispherically models obtained from independent inversions of these two distinct anisotropy, previously proposed on the basis of data sets differ significantly suggest that this is not the case. body wave measurements [e.g., Tanaka and Hamaguchi, [7] The BC arrivals are observed in the 145 to 153 1997; Creager, 1999; Niu and Wen, 2001]. Normal modes epicentral distance range (Figure 1), and the corresponding do not constrain this type of structure, because they are only BC DF data are sensitive to inner core structure down to sensitive to even-degree anomalies. Focusing on absolute roughly 300 km beneath the ICB. There are 851 BC DF body wave data, we investigate if large-scale variations, measurements in our data set, spanning the distance from including hemispheric variation, in inner core anisotropy 145 to 160 . Data with an epicentral distance greater than can be observed consistently. We use both normal mode and 153 involve diffracted BC traveling along the ICB. We body wave data to constrain the global average and consider discard these data when performing inversions but return to hemispheric deviations as perturbations from this average. them in section 4, where we consider structure near the ICB. [5] In general, inner core models derived using absolute The remaining 512 BC DF data are binned into two and differential travel time data differ most in their level of distance ranges, 145 to 150 and 150 to 153 ,and anisotropy. Models based upon differential travel times have averaged for each 0.1 increment in cos2 x, where x is the strong anisotropy [e.g., Creager, 1992; Song and Helm- angle between the direction of wave propagation and the berger, 1993], especially near the center of the Earth [e.g., symmetry axis of transverse isotropy. The averaging process ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 3 reduces the effects of mantle heterogeneity by cancelling out the isotropic signal if the outer core entry and exit positions of BC or AB cover the globe uniformly. In this paper we show that differential travel time data coverage is uneven compared to absolute travel time data, and suggest biased sampling as the reason for difference in inner core models derived from these two data sets. [8] We compare BC DF data in the range from 150 to 153 with DF from the same distance range (Figure 2a). The two sets of data agree well in general, except for 4 points at values of cos2 x of 0.45, 0.55, 0.75, and 0.85. The averages of BC DF at these points seem to be well constrained by clusters of measurements around values of cos2 x of 0.5 and 0.8. However, upon inspection of source-receiver pairs, we find that the cluster about cos2 x = 0.8 is due to a path between South Sandwich Islands and Alaska. Data from this path are known to be anomalous [e.g., Su and Dziewon´ski, 1995; Dziewon´ski and Su, 1998], and the exclusion of these data changes both BC DF and DF values, although the change in BC DF data is greater than in DF. The data sets agree better now at cos2 x of 0.75 and 0.85 (Figure 2b). We also find that the cluster at about cos2 x = 0.5 is mainly due to two earthquakes south of Africa recorded at 71 stations in California. If we remove this cluster (Figure 2c), the agree- ment between DF and BC DF data is remarkable. Further- more, the constant model of anisotropy obtained in paper 1 fits both sets of body wave data. In inversions constrained only by, or relying heavily upon, the differential travel times, these anomalous data are up-weighted due to abundant measurements, and would produce a model with strong anisotropy. This is evident in Figure 3 of paper 1. The model of Creager [1992] fits the anomalous data associated with the paths between South Sandwich Islands to Alaska at the expense of poorly fitting the data at higher values of cos2 x. Note that the cluster of measurements from the earthquake south of Africa were not available to Creager [1992], since the earthquake occurred on 29 March 1993. [9] To complement the BC DF data, which are sensitive Figure 2. (a) Comparison of mantle-corrected DF data only to shallow structure of the inner core, measurements of (circles) and BC DF data (triangles) in the distance range AB DF data between 145 and 176 (Figure 1, right) are 150 –153 . To ease visual comparison, the sign of the DF often included in inner core inversions [e.g., Vinnik et al., data has been reversed, and a baseline shift has been applied 1994; Song and Helmberger, 1995; Song, 1996; McSweeney (we are interested in the trend in the data as shown in et al., 1997; Creager, 1999]. Because the paths of AB and DF equation (6) of paper 1). The background dots are individual differ significantly in the mantle (Figure 1, left), contami- BC DF measurement, and the solid curve is the prediction nation of AB DF with structure in the lowermost mantle has based upon the constant anisotropy model derived in paper been suggested [e.g., Breger et al., 1999, 2000], but is 1. (b) Same as in Figure 2a, except that the data from the ignored in inner core studies [e.g., Vinnik et al., 1994; Song path between South Sandwich Islands and Alaska have been and Helmberger, 1995; Song, 1996; McSweeney et al., 1997; removed. (c) Same as in Figure 2b, except that in addition to Creager, 1999]. We will investigate the effect of the mantle the data from the path between South Sandwich Islands and on AB DF and BC DF in a later section. Alaska, the data from two earthquakes located south of [10] We group AB DF data into four distance ranges, Africa and stations in California are removed. 149 to 153 , 153 to 160 , 160 to 165 , and 165 to 180 . Data in each distance range are averaged for every 0.1 increment in cos2 x. We compare AB DF and DF in the recorded at 35 stations in Alaska. Removal of this earth- range 160 to 165 in Figure 3a. In general, the two types of quake (Figure 3b) does not improve the compatibility of data agree well, which is surprising considering the like- AB DF and DF, but since the average at cos2 x = 0.75 is lihood of strong contamination from the mantle. The only determined by a single datum, it is possible that this exception is at cos2 x = 0.75, where the AB DF average discrepancy reflects either another anomalous path or sub- seems to be well constrained by numerous points between stantial mantle heterogeneity or source mislocation. Very cos2 x values of 0.7 and 0.8. However, as for BC DF, strong anisotropy near the center of the inner core, inferred examination of these points reveals that they originate, with in many differential travel time studies [e.g., Vinnik et al., one exception, from a single earthquake near Bouvet Island 1994; Song and Helmberger, 1995; Song, 1996; McSweeney ESE 21 - 4 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2
of the inner core (Figure 3 of paper 1). The origin of the anomalous differential travel times may also be attributed to small-scale structure [e.g., Creager, 1997; Dziewon´ski, 2000; Vidale and Earle, 2000] or lateral variations in the inner core [e.g., Su and Dziewon´ski, 1995].
3. Inversion for Inner Core Models
[12] In this section, we assume that the anomalous differ- ential data originate in the inner core, and investigate if
Figure 3. (a) Comparison of mantle-corrected DF data (circles) and AB DF data (triangles) in the distance range 160 –165 . There are no measurements of AB DF with cos2 x greater than 0.8 in this distance range. To ease visual comparison the sign of DF has been reversed, and a baseline shift has been applied. The background dots are individual differential AB DF measurement. (b) Same as in Figure 3a, except that the data from an earthquake near Bouvet Island recorded at stations in Alaska are removed. et al., 1997; Creager, 1999], is the result of trying to fit the large AB DF residuals at large cos2 x. [11] These comparisons demonstrate the biased sampling of the Earth by the differential travel time data. To quantify this, Figure 4 shows the coverage of the inner core with the entire set of BC DF, AB DF, and DF data in terms of bottoming point. Most of the inner core is not sampled by Figure 4. Plot of all bottoming points for (top) BC DF, the differential travel time measurements, but it is well (middle) AB DF, and (bottom) DF data. This plot is made sampled by DF data except for some spots in the South using data from all distances (between 145 and 153 for Atlantic. Therefore DF data should represent global aniso- BC DF data, between 149 and 180 for AB DF data, and tropy better than differential data, and this explains why DF between 120 and 140 and between 150 and 180 for DF data are highly compatible with normal mode data (paper data). Note that DF and combination of two differential 1). In addition, at angles where biased data dominate the travel time data sets have been used to derive anisotropic average values, effects due to variations in the mantle are model of the whole inner core. In later figures, we show that unlikely to have been cancelled. This may explain why coverage degrades substantially when we start investigating anomalous differential data are poorly fit by a simple model depth and lateral dependence of anisotropy. ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 5
differential travel time data. Mantle-corrected DF data at an epicentral distance range less than 153 also exhibit a rapid decrease in variance reduction. Therefore data from rays shallowly penetrating the inner core do not favor the existence of an isotropic layer. In contrast, the fit to data such as AB DF and DF at large epicentral distances varies only slightly with the introduction of an isotropic layer and is highly compatible with a layer as thick as 150 km from the ICB; however, their sensitivity to shallow structure is less, and the fit is achieved by slightly modifying the strength of anisotropy in the deeper part. These observations are robust and they do not depend upon the maximum radial expansion or the type of basis function used. There are at least two possible explanations for poor fits to data at small distance ranges. The first is that the weak angle-dependent trend observed in data at these distances is due to inadequate mantle corrections. However, the averaging procedure and Figure 5. Fit to splitting function coefficients of inner core comparison of Figures 5 and 6 of Su and Dziewon´ski [1995] sensitive modes as a function of the thickness of the suggest that this is unlikely for data in the distance range of isotropic layer from the ICB. The variance reduction is 130 –140 . The second, and our preferred, explanation is obtained from an inversion with an S velocity, P velocity, that the inner core is anisotropic near the ICB. Our model and density parameterization within the mantle, and with 1.8% anisotropy gives good fit to DF data in the 130 – assuming constant anisotropy within the inner core below 140 range. the isotropic layer. [15] The data set with the most sensitivity to the shallow part of the inner core does not support the existence of an isotropic layer near the ICB. Can this observation be complex structures, such as an isotropic layer near the ICB integrated with data from which inferences of isotropic and hemispherically dependent anisotropy, can provide a layer have been made? The concept of an isotropic layer model that fits both DF and differential travel time data. was introduced based upon Shearer’s [1994] study which Although we focus on body wave data, all inversions rejected a high (3.5%) level of anisotropy using absolute include normal mode splitting functions. Because a constant travel time data at short distances (132 to 140 ). This model of anisotropy fits the data well (paper 1), we conclusion appears to have been misinterpreted as an argu- assume constant anisotropy in this section, unless otherwise ment for an isotropic layer near the ICB [Song and indicated. Helmberger, 1998]. Our global anisotropy model achieves a satisfactory fit to Shearer’s data set in this distance range 3.1. Isotropic Layer Near the Inner Core Boundary (Figure 6): indeed, a better fit than weak anisotropy model [13] There have been suggestions that anisotropy in the of Shearer et al. [1988]. None-zero anisotropy near the ICB inner core is weak in the top 50–300 km [e.g., Shearer, is not inconsistent with differential travel time data as it may 1994; Song and Helmberger, 1995; Creager, 2000], or that appear at first. Although isotropy is strongly advocated, this region is isotropic [Song and Helmberger, 1998]. To differential travel times do not rule out the presence of weak investigate if the hypothesis of an isotropic layer is compat- ( 1%) anisotropy near the ICB [e.g., Song and Helmberger, ible with mode and DF data, we perform inversions in 1995; Creager, 2000; Garcia and Souriau, 2000]. Therefore which an isotropic layer of varying thickness is imposed anisotropy at the topmost inner core would explain DF data near the ICB. The fit to the mode data as a function of the at short distances and is consistent with differential travel thickness of the isotropic layer is shown in Figure 5. The fit time data as long as it is relatively weak. Finally, we present improves marginally as the thickness is increased to about additional evidence for finite anisotropy near the ICB using 100 km, however the improvement is not statistically diffracted BC DF data in section 4. significant. A significant drop in variance reduction starts around 150 km. We conclude that normal mode data are 3.2. Large-Scale Variations in Anisotropy consistent with an isotropic layer up to about 150 km [16] Inner core sensitive normal modes do not seem to thickness, in agreement with Durek and Romanowicz require complicated structure within the inner core (paper [1999]. 1). However, several studies based upon differential travel [14] When the fit to DF travel time data is considered, the time data [e.g., Tanaka and Hamaguchi, 1997; Creager, overall variance reduction decreases monotonically with 1999; Niu and Wen, 2001] have suggested that the proper- increasing thickness of the isotropic layer. The most sig- ties of the inner core have an east-west hemispherical nificant change is observed in the fit to BC DF data: dependence. The normal mode data are insensitive to the introduction of an isotropic layer immediately decreases hemispherical difference since such a pattern corresponds to the variance reduction and the fit degrades rapidly when the structure at spherical harmonic degree one. Only body wave thickness is more than 30 km. The degradation of fit data are sensitive to hemispheric differences; hence we contradicts previous differential travel time studies, how- focus our attention to the travel time data. We investigate ever, it is due to normal mode constraint: modes do not if data are consistent with such large-scale structure by allow strong anisotropy in the interior as required by dividing the data into subsets based upon their bottoming ESE 21 - 6 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2
western hemisphere. This is partly due to the separation of two clusters into different hemispheres, one associated with the south of Africa-California path (cos2 x 0.5) and another with the South Sandwich Islands-Alaska path (cos2 x 0.8), but also because there are only a few measure- ments in the southern hemisphere with small values of cos2 x. Difference between eastern and western hemispheres is not clear for BC DF data between 145 and 150 . Division of data into northern and southern hemispheres seems to enhance hemispheric differences at this distance range. However, there are only nine measurements above a cos2 x of 0.2 for the southern hemisphere, so little significance can be attributed to the slightly larger difference between the northern and southern hemispheres. In contrast to DF and BC DF data, the difference between eastern and western or northern and southern hemispheres is not obvious for AB DF data in general (e.g., Figures 7e and 7f ). The difference appears slightly more pronounced for Figure 6. ISC summary ray residuals for the distance the north-south division, however, it is difficult to compare range 132 to 140 (P. M. Shearer, personal communica- the two subsets as the distribution of data seems to comple- tions, 2001). The residuals are plotted as a function of 90 ment one another: where there are many measurements in x rather than cos2 x to ease comparison with Figure 9 of one hemisphere, there are only a handful of measurements Shearer [1994]. The standard deviation associated with each for the other. It is, nonetheless, consistent with DF or datum is shown as a vertical bar. Predictions based upon BC DF data in that the stronger anisotropy trend can be models from Shearer et al. [1988], Creager [1992], and the associated with the northern or western hemisphere. constant anisotropy model of paper 1 [Ishii et al., 2002] are [19] Inversions using hemispherically divided data sets shown. Note that the strong anisotropy in Creager’s model produce only marginal improvement in fit including differ- overpredicts residuals at high values of x. Data courtesy of ential travel time data. Hemispheric anisotropy model for P. Shearer. the eastern and the western hemispheres differ considerably, especially for the poorly constrained parameter s. Even if we accept the possibility of hemispheric variations for a points. The eastern and western hemisphere data show clear slowly growing crystal within a homogeneous liquid difference, but such dichotomy is also observed when the [Jacobs, 1953], it will be difficult to explain such a large inner core is divided into the northern and southern hemi- deviation physically. Although dependence of anisotropy spheres. We present a geometrical argument that the appa- with latitude may be more physically plausible than depend- rent hemispheric anomalies result from a localized region, ence on longitude, inversions for different anisotropy in the and much of data can be explained by our constant northern and southern hemispheres do not produce satisfac- anisotropy model. tory fits. Because the data trend is smoother with respect to 3.2.1. Hemispheric Dependence of Anisotropy cos2 x than with a east-west division, one might expect [17] Although investigations of hemispheric dependence better fits for the northern and southern data. However, the of anisotropy concentrated on east-west difference [e.g., divergence of hemispheric data is too rapid at large cos2 x Tanaka and Hamaguchi, 1997; Creager, 1999; Niu and and is inconsistent with the data trend at small values of Wen, 2001], the division of the inner core into eastern and cos2 x. In section 3.2.2, we investigate the property of data western hemispheres is not the only way in which one can with large cos2 x values. obtain subsets with distinct behavior. We demonstrate this 3.2.2. Data Distribution and Hemispheric Dependence effect by separating data according to whether they bottom [20] When we group the data into hemispheres, especially in the northern or southern hemispheres. A clear difference into the eastern and western hemispheres, the travel times between hemispheres is observed regardless of the defini- diverge rapidly at around cos2 x = 0.7. Such an increase in tion of hemisphere for DF data (Figures 7a and 7b). In the gradient of travel times is inconsistent with a trans- general, the hemispheric data agree well with one another in versely anisotropic inner core where travel time depends the distance range from 120 to 140 . In addition, there is a quadratically on cos2 x (equation (5) of paper 1). Therefore good agreement between hemispheres when cos2 x <0.7 a difference in the strength of anisotropy is not sufficient to over all distance ranges. Because large differences are explain unambiguously the observed change in gradient. observed only at high values of cos2 x, where there are Another observation from separating the inner core into inherently less data, it is possible that the differences are due hemispheres is that the difference becomes significant when to poorer sampling and local structure. For example, biased cos2 x is above 0.7. The smallest angle x (hence largest cos2 sampling of an anomalous region of the inner core or mantle x) for a ray occurs when it is traveling in the north-south heterogeneity not included in our mantle correction can plane perpendicular to the equatorial plane. This geometry create apparent hemispheric differences. is such that the smallest angle x is equal to the latitude of the [18] When hemispheric BC DF data are compared (Fig- bottoming point (Figure 8a). The relationship between the ures 7c and 7d), a smoother variation as a function of cos2 x latitude of the bottoming point and the largest cos2 x is is observed again for the northern hemisphere than the plotted in Figure 8b. Clearly, the data with high values of ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 7
Figure 7. Comparison of data from eastern/western hemispheres and northern/southern hemispheres. (a) and (b) Comparison of DF data in the distance range between 153 and 155 . The inner core is divided into eastern (solid triangles) and western (shaded circles) hemispheres in Figure 7a, while it is divided into northern (solid triangles) and southern (shaded circles) hemispheres in Figure 7b. (c) and (d) Same as Figures 7a and 7b except that BC DF data are compared at the distance range between 150 and 153 . The small triangles and circles are individual measurements. Note that there are no data between cos2 x of 0.2 and 0.4 for the southern hemisphere and between 0.9 and 1.0 for northern hemisphere. (e) and (f ) Same as Figures 7c and 7d except that AB DF data are compared at the distance range of 153 and 160 . There are no data between cos2 x of 0.6 and 0.7 and between 0.9 and 1.0 for the western hemisphere, between 0.8 and 0.9 for the eastern hemisphere, between 0.5 and 0.6 for the northern hemisphere, and between 0.8 and 1.0 for the southern hemisphere. ESE 21 - 8 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 cos2 x come only from rays bottoming near the equator data. In passing, we note that the two anomalous BC DF while those with small cos2 x values bottom at all latitudes. paths, south of Africa to California and South Sandwich [21] We divide our DF data set into four subsets: eastern Islands to Alaska, both bottom in the western equatorial polar, eastern equatorial, western polar and western equa- region. torial regions (Figure 8c). Separating differential travel [22] To ease comparison between the quadrants, we only time data into quadrants reduces the number of measure- show data between cos2 x of 0.0 and 0.7 (Figure 9). Data ments so much that it is difficult to study data trend as a from different quadrants generally agree in their trend (slope function of cos2 x. Therefore we concentrate on the DF and curvature). Note the good agreement particularly at distance ranges (150 –153 , 153 –155 , and 155 –160 ) where a strong east-west hemispheric difference is observed. Moreover, the data trends from all quadrants agree surpris- ingly well with the prediction from the constant anisotropy model obtained in paper 1. This suggests that a global anisotropy model can explain much of the data even if they are divided into hemispheres or quadrants. The only excep- tion is 175 –180 distance range which is investigated by Ishii and Dziewon´ski [2002]. Comparison of bottoming locations for data with cos2 x above and below 0.7 indicates that high values of cos2 x are constrained unavoidably by a much smaller number of data which bottom in regions where coverage by data with smaller values of cos2 x is not very good (Figure 10a). This is particularly true for the western hemisphere where large travel time residuals are observed. Because of the relatively small size of the database, cos2 x > 0.7 values are affected more by source-receiver pairs with large residuals (Figure 10b). [23] The ambiguity of hemispherically dependent aniso- tropy is demonstrated further when data are binned to make summary rays depending upon the distance range, the ray angle with respect to the symmetry axis, and the bottoming point. One example from 153 –155 , which is the distance range where hemispheric difference is most prominent, is shown in Figure 11. This approach highlights the uneven distribution of data for all values of cos2 x, indicating the difficulties of assessing lateral variations in anisotropy. Hemispheric dependence, be it east-west or north-south, can not be clearly identified with such sparse data set. We
Figure 8. (opposite) Geometry of DF in the inner core and its implications for bottoming latitude. (a) The relationship between the latitude of the bottoming point of the ray (q0) and the smallest value of the ray angle with respect to the rotation axis (x). At the bottoming point, the ray (solid red line) is perpendicular to the unit vector in radius. This implies that x + q =90 , where q is colatitude and hence x = q0. (b) Plot of the latitude of ray’s bottoming point (y axis) against cos2 x. The solid curve shows maximum latitude as a function of cos2 x. The dots show where individual DF datum between 150 and 153 distance range plots. Streaks of dots are the results of an earthquake observed at various stations and/or a station observing a suite of earthquakes at similar locations. (c) Division of DF data into eastern polar region (jlatitudej >30 with 0 longitude < 180 , indicated by green dots), eastern equatorial region (jlatitudej30 with 0 longitude < 180 , blue dots), western polar region (jlatitudej >30 with 180 longitude < 360 , yellow dots), and western equatorial region (jlatitudej30 with 180 longitude < 360 , red dots). Dots on the map are bottoming points of DF data in the 150 to 153 distance range. ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 9
Figure 9. Comparisons of subsets of DF data at various distance ranges. Data with different colors correspond to quadrants as shown in Figure 8c. Data with cos2 x > 0.65 are available for the two equatorial regions; however, we truncated the data at 0.65 to ease comparison between quadrants. The black curve is the prediction based upon constant anisotropy model obtained in paper 1. Note that data from 173 –180 distance range behave differently compared to other distances [Ishii and Dziewon´ski, 2002]. ESE 21 - 10 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2
Figure 10. (a) Comparison of bottoming point distribution for data with cos2 x smaller and greater than 0.7 in the distance range between 150 and 153 . (b) Comparison of eastern (grey curve with triangles) and western (black curve with squares) subsets of data at 150 –153 distance range. When the data from the anomalous path between South Sandwich Islands and Alaska are removed from the western data (black dotted curve between 0.65 and 0.95), the difference between the eastern and western hemispheres is smaller. conclude that the hemispheric difference is only apparent. data: 83% and 85%, respectively. In contrast, fitting differ- Most of the data at values of cos2 x 0.7 are consistent ential data is more difficult, and variance reductions for with the global anisotropy model, suggesting that the hemi- these data are lower although these data should be of higher spheric discrepancy is due to a smaller-scale phenomenon. quality than DF data: 71% for BC DF and 74% for The apparent hemispheric difference is explained easily if AB DF (paper 1). Previous studies [Breger et al., 1999, small structures are located in the inner core, however, 2000; Tkalcˇic´etal., 2002] have suggested that this may be because of the limited number of paths with cos2 x >0.7 due to heterogeneity in the lowermost mantle, where the and uneven coverage, the possibility of effects from the paths of BC and DF or AB and DF differ considerably. For mantle cannot be dismissed. the rest of this section, we assume constant anisotropy in the inner core based upon paper 1 and investigate if the residual signal can be associated with structure of the lowermost 4. Discussion mantle. [24] We have seen that allowing for complexities, such as [26] Using the constant anisotropy model (paper 1), we hemispheric variations and an isotropic layer near the ICB, predict the travel time for the differential data. Any devia- does not improve the fit to differential data substantially. In tions of a measurement from these predictions are then section 4.1, we return to a simple model of inner core placed at the outer core entry and exit points of the BC or anisotropy and investigate if the misfit to differential data AB ray. The inherent assumption is that the deviations can be explained by structure in the lowermost mantle. Then originate in the outer core branch. Therefore we associate we look briefly at differential data that were not used in the positive residuals with slower velocity and negative resid- inversions: diffracted BC DF. uals with faster velocity and calculate the average of residuals for each 10 by 10 block. Note that positive 4.1. Residual Differential Body Wave Data anomalies, if ascribed to the DF part of the differential data, [25] Finding a constant anisotropy model that fits both imply faster than average velocity and negative anomalies normal mode and DF data is very easy and the variance indicate slower than average velocity in the inner core. This reductions obtained from such a model are high for these procedure does not consider the spread of residuals along ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 11
Figure 11. Plot of DF residuals as a function of ray angle and bottoming location. For each plot, average has been removed to enhance lateral variations. Unusually large residuals are due to bins with only one or two measurements. Using triangular tessellation, the center of each bin is obtained from dividing the Earth into 362 nearly equal-area triangles as in Figure 1 of Gu et al. [2001]. Radius of each bin is 10 . the ray path of BC or AB. Nevertheless, we still believe that map view of BC DF after inner core corrections, in the resulting maps give an indication of the importance of contrast, is highly nonzonal. There are still some strong mantle structure near the CMB. features, such as a positive (slow if due to BC) anomaly in [27] Figure 12a shows the hit count and residual map of the South Pacific and a negative (fast) anomaly between BC DF. The hit count map shows a very biased distribu- South America and Antarctica. However, the amplitude of tion. Much of the globe is poorly sampled (regions in black) these anomalies is much lower compared to a map without as expected from Figure 4, with few exceptions. For inner core corrections. example, the high counts under north-western Canada and [28] Although we have more AB DF data, Figure 12b the southern Atlantic are due to BC DF measurements of shows that they still come from limited source-receiver earthquakes from the South Sandwich Islands recorded at pairs; these data cover the globe unevenly, with a bias stations in Alaska. Similarly, the paths from the two earth- toward the western hemisphere. This bias implies that quakes south of Africa to numerous stations in California AB DF data, which are more sensitive to mantle structure appear as high counts near Antarctica and the southwestern than BC DF, sample only certain parts of lowermost United States. The strongest features in the map of BC DF mantle. Therefore the averaging procedure is insufficient travel times without inner core corrections are the three red to cancel out the mantle contribution. The zonal pattern in spots (positive residuals) around the southern Atlantic, the uncorrected travel time map (evident in Figure 12a) is Alaska, and the southern Pacific. These are due to measure- not present for AB DF, and the pattern looks similar to the ments of anomalies from polar paths. The large-scale and corrected BC DF map. AB DF after inner core correc- the strongest feature in this map is a zonal pattern, i.e., tions appears virtually identical to the uncorrected map, positive anomalies (red to yellow) at high latitudes and although inner core corrections reduce the amplitude of the negative (blue to green) anomalies near the equator. The residuals. AB is a ray that grazes the CMB (Figure 1); a ESE 21 - 12 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2
Figure 12. (a) (top) Hit count map for BC DF measurements. Black regions indicate poor sampling and white indicate well-sampled regions. This map shows that BC DF data illuminate only a limited part of the mantle. Note that compared to conventional seismic tomography of the mantle or DF measurements from ISC, the number of data is much smaller. The numbers on the scale are the number of rays instead of its logarithm. (middle) Map view of BC DF measurements plotted at the entry and exit points of BC. Red regions indicate places with positive travel time anomalies (if attributed to BC, this corresponds to slower than average velocity in the mantle), and blue regions indicate negative anomalies (fast velocity). (bottom) Map view of BC DF measurements after correcting for the inner core signal using a constant model of anisotropy. The residuals are plotted at the entry and exit points of BC. The scale is the same as the middle panel. (b) Same as in Figure 12a except for AB DF measurements. region known to be highly heterogeneous. Hence it is not have fast velocity anomalies in this region, with some surprising that AB DF data contain strong signals from exceptions, such as the S velocity model of Su and Dzie- mantle heterogeneity [Breger et al., 1999, 2000]. won´ski [1997], which has close to zero value, and the P [29] The inner core corrected residual patterns for BC DF velocity model of van der Hilst et al. [1998] with a negative (Figure 12a) and AB DF (Figure 12b) are very similar in velocity anomaly underneath Alaska. The D00 model of regions that are well sampled. This similarity suggests that Tkalcˇic´etal.[2002], based upon PcP P and differential these signals originate in the lowermost mantle. The differ- data, also shows a negative velocity anomaly under Canada. ence in amplitude likely arises from the path difference This anomaly contributes to the large positive BC DF between BC and AB. AB spends more time in this strongly measurements for the path between South Sandwich Islands heterogeneous layer, hence it is affected more by mantle to Alaska (Figure 2). structure near the CMB. Some of the features observed in [30] The main difference between the maps shown in the residual maps are consistent with P velocity models near Figure 12 and the structure obtained by Tkalcˇic´etal.[2002] the CMB, such as the fast anomaly under India and eastern is the strength of the anomalies. The residual maps of Asia, and the slow anomaly in the southern Pacific ocean. BC DF and AB DF generally have an amplitude of The fast, linear anomaly in the northern Pacific is also ±1.5 s. If we assume that the signal originates from ray consistent with some P velocity models [e.g., Vasco and paths with a length of 300 km in the mantle, and the average Johnson,1998;van der Hilst et al.,1998;Boschi and P velocity is 13.5 km/s, then a simple conversion gives Dziewon´ski, 1999; Karason and van der Hilst, 2001] and approximately ±7% variations for ±1.5 s. Our calculations some S velocity models [e.g., Gu et al., 2001]. However, do not consider the geometry and length of the BC or AB there are features in the residual maps, such as a slow ray path, so this estimate is likely to be an overestimate. velocity anomaly under Canada and Alaska, that are not Most recent P velocity models [e.g., Bolton, 1996; Boschi observed in tomographic models. Most tomographic models and Dziewon´ski, 1999] have amplitudes of ±1% and so does ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 13 the D00 model of Tkalcˇic´etal.[2002], although the latter includes anomalies in excess of ±2.5%. Nonetheless, ampli- tudes as large as ±7% have been observed near the CMB using diffracted P waves [Sylvander et al., 1997], and the locations of slow velocity anomalies in the residual maps (Figure 12) correspond well with observations of ultralow- velocity zones (ULVZs), for example, underneath southern Pacific and Africa [e.g., Mori and Helmberger, 1995; Garnero and Helmberger, 1996; Vidale and Hedlin, 1998; Garnero et al., 1998]. [31] The residual patterns, especially that of AB DF, agree remarkably well with the P velocity model within D00 of Tkalcˇic´etal.[2002]. These observations indicate that most of the differential anomaly that is not reconciled by a constant anisotropy model of the inner core results from heterogeneity deep within the mantle. The strong anisotropy in inner core models derived from differential travel time data is due to local anomalies or structure near D00.In particular, anisotropy near the center of the Earth is con- strained only by a heavily contaminated AB DF data set, making inferences of increased anisotropy in the deepest part of the inner core questionable. Inverting for inner core structure using normal mode, absolute, and differential travel time data allows us to separate mantle and inner core effects. [32] How would such a strongly heterogeneous layer near the CMB affect DF and normal mode data? The P velocity model used to correct DF for mantle structure does not include this layer nor does the model derived from the mode inversion. Because DF data have better coverage, and since they are almost vertical when they enter or exit the core, the effect of the layer near the CMB will be small and is likely to be cancelled out by the averaging procedure. Similarly, deeply-penetrating modes have a broad kernel near the CMB, and the splitting due to this layer will not be substantial. Furthermore, the zonal component of the het- erogeneity is relatively small; hence the effect on the zonal Figure 13. (a) Plot of BC DF residuals after correcting part of the splitting function will be limited. On the other for constant anisotropy in the inner core (x axis) and hand, the nonzonal residual of inner core sensitive modes travel time anomalies predicted by mantle heterogeneity (Figure 7 of paper 1), may be a result of this strongly based upon the recent P velocity model of Antolik et al. heterogeneous layer. Therefore mantle structure near the [2002] (y axis). The grey dots are for a path between the CMB must be considered, but it does not significantly South Sandwich Islands and Alaska, open circles are for affect the analysis of inner core anisotropy presented in a path between south of Africa and California and black paper 1. dots are for other paths. (b) Same as in Figure 13a except for the AB DF residual. The shaded dots are for a path 4.2. Mantle Heterogeneity and Anomalous Paths between the South Sandwich Islands and Alaska, and [33] There are numerous observations of differential open circles are for a path between Bouvet Island and travel times for the path between South Sandwich Islands California. to Alaska, which have been used to derive global models [e.g., Creager, 1992], laterally varying models [e.g., Cre- ager, 1997], and differential rotation of the inner core [e.g., [34] We address the issue of a possible mantle signal in Song and Richards, 1996; Su et al., 1996; Creager, 1997]. differential travel times by comparing the differential travel Furthermore, observations of DF from this path led Su and time residuals (after correcting for constant anisotropy in Dziewon´ski [1995] to estimate the tilt of the symmetry axis the inner core) with predicted differential travel times from to be 11 , which was later shown to have been an a recent three-dimensional mantle model [Antolik et al., overestimate biased by this path [Souriau et al., 1997; 2002]. The results for BC DF and AB DF are shown in Dziewon´ski, 2000]. In preceding sections, we have shown Figure 13. In general, the predicted residual due to mantle that this path is highly anomalous and that the measure- structure is much smaller than the observed residuals, ments do not reflect global anisotropy. Large deviations in consistent with the results of Breger et al. [1999, 2000]. BC DF differential travel time data suggest that the It suggests that the amplitude of the P velocity models of anomaly is mostly within the inner core, although part of the lowermost mantle is under-estimated as already docu- the anomaly can be explained by an inadequate mantle mented for S velocity models [e.g., Ritsema et al., 1998; correction. Breger and Romanowicz, 1998]. For BC DF, there is no ESE 21 - 14 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 correlation between observed and predicted residuals if the entire data set is considered, but if measurements from the two anomalous paths identified in section 4.1 are removed, the data are slightly correlated. The large residuals from the anomalous paths from the South Sandwich Islands to Alaska and from south of Africa to California deviate far from the main cluster. A similar comparison for AB DF data exhibits a stronger correlation between predictions and observations, indicating that mantle structure is impor- tant for this data set. The South Sandwich Islands to Alaska path does not stand out as particularly anomalous, but Bouvet Island to California produces a cluster away from the origin. Creager [1999] performed a similar experiment using a mantle model by Karason and van der Hilst [2001] and compared its predictions with BC DF and AB DF. He found no significant correlation between data and prediction from the mantle model. However, Creager did not correct for inner core aniso- tropy; hence the poor correlation may be due to inner core effect obscuring mantle signal or under-estimated mantle structure near the CMB. [35] Comparison of predictions based upon a three- dimensional mantle model and residuals after inner core anisotropy correction confirms the importance of a mantle correction and emphasizes the existence of paths with highly anomalous data, especially the path between South Sandwich Islands and Alaska. Small-scale variations in the inner core can explain anomalous data, but effects such as due to slabs [Helffrich and Sacks, 1994] should also be considered. Our experiments with mantle models based upon convection simulations [Pysklywec and Mitrovica, 1998] suggest that slabs are capable of producing differ- ential travel time residuals comparable to and sometimes even larger than residuals due to small-scale heterogeneity near the CMB. Furthermore, the South Sandwich Islands to Alaska path samples the inner core only in one direction: there are no paths sampling that particular region of the Figure 14. (a) Comparison of BC DF data from 150 to inner core with other azimuths. Therefore it is not clear if 153 (triangles) and diffracted BC DF data from 153 to anomalous measurements from this path are associated with 155 (circles). The shaded dots in the background are anisotropy. individual measurements of diffracted BC DF. (b) Same as in Figure 14a, except that the anomalous path from South 4.3. Diffracted BC DF Data Sandwich Islands to Alaska has been removed. [36] Because most BC DF measurements at distance greater than 153 use diffracted BC, we have not included these data in our inversions. We now investigate if these smoothly, the data from 153 to 155 should have com- data can be used to constrain inner core structure near the patible or larger travel time anomalies than those from ICB. The measurements using diffracted BC are compared 150 to 153 . A drastic change in anisotropy in the with BC DF data at shorter distance ranges in Figure 14. incremental 36 km may allow smaller anomalies at larger Most of the diffracted BC DF data (209 measurements out distance, but our inversions for layered inner core aniso- of 339) are within the distance range from 153 to 155 . tropy models position interfaces at other depths (paper 1). The residuals are generally smaller (closer to zero) than If anisotropy is constant, the model of Creager [1992], BC DF from 150 to 153 , except when cos2 x = 0.85. which fits the BC DF data well, should give a reasonable Diffracted BC DF data have a smaller slope and curvature fit to data in the 153 to 155 distance range, but it as a smooth function of cos2 x, indicating that anisotropy overpredicts the residuals significantly. This evidence sensed by this data set is weaker than that from BC DF suggests that the missing signals are due to the diffracted without diffraction. This is even more evident when the BC ray sampling the uppermost part of the inner core. The anomalous path from South Sandwich Islands to Alaska is evanescent wave does not penetrate deeply into the inner omitted (Figure 14b). core, but the accumulation of signal along approximately [37] The average bottoming depth for data in the dis- 50 km of the ICB will be significant, and comparable to tance range from 150 to 153 is 250 km, and it is 286 km the signal observed in the 120 to 130 distance range. It for data in the range 153 to 155 . If diffracted BC is appears that anisotropy near the ICB is required in order to insensitive to the inner core and anisotropy is varying explain the diffracted BC DF data, in addition to the ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 15 observed trend of DF data between 130 and 140 distance [40] We also considered the possibility of a large-scale range. dependence of anisotropy, relying in this effort upon body wave data. Hemispherically averaged data show a distinct behavior between the eastern and western hemispheres, but 5. Conclusions the number of measurements used for each hemisphere differ [38] In paper 1 we found that normal mode and mantle- greatly, and it is not clear how much of the hemispheric corrected DF data are highly compatible, but BC DF and discrepancy originates from biased sampling. The inversion AB DF differential travel time data differ slightly. Com- results show an unreasonably large difference between parison of DF and BC DF or AB DF data shows that this hemispheres, and overall improvements in fit are only may be due to biased sampling. The absolute and differ- marginal. Furthermore, the division of the inner core into ential travel time measurements disagree strongly whenever eastern and western hemispheres is somewhat artificial: a there is a cluster of differential data from a particular difference in data can also be obtained if the inner core is source-receiver pair. These clusters of data seem to drive divided into northern and southern hemispheres. On the inferences of very strong anisotropy in the inner core based other hand, the data from two hemispheres are similar at upon differential measurements. In addition, differential small values of cos2 x and diverge almost discontinuously at data sample a limited part of the mantle and the inner large values of cos2 x regardless of hemispheric division. core, whereas DF data have better coverage and hence Using a geometrical argument, we divide the inner core into average isotropic mantle structure more effectively. This quadrants and show that data with large cos2 x originate from global sampling by DF explains why the normal mode rays bottoming near the equator, hence localizing the source data, which are global by definition, are more consistent of apparent hemispheric difference to a much smaller region. with DF data than with differential travel time data. Moreover, the simple model of anisotropy obtained in paper Because of this agreement between normal mode and DF 1 is equally valid for all quadrants when data with cos2 x < data, the source of anomalous measurements of BC DF or 0.7 are considered, suggesting that the inner core anisotropy AB DF must be heterogeneity within the inner core [e.g., is laterally homogeneous at large scales. Creager, 1997; Dziewon´ski, 2000; Vidale and Earle, 2000] [41] Because these complexities fail to improve the fit to or to lateral variations within the mantle [Breger et al., differential data while maintaining a good fit to normal mode 1999, 2000; Tkalcˇic´etal., 2002] which are small enough and absolute travel time data, we investigate if the unmodeled that they do not substantially affect average structure of the part of differential data can be placed in the mantle. A simple inner core. procedure of assigning the residual signal of differential data [39] Our preferred model of constant anisotropy (paper (i.e., after correction using a constant model of inner core 1) contradicts the hypothesis that the inner core is isotropic anisotropy) to exit and entry points produces similar maps for near the ICB [e.g., Song and Helmberger, 1998; Ouzounis BC DF and AB DF. In addition, these maps are highly and Creager, 2001; Song and Xu, 2002]. We investigate compatible with a recent study of P velocity structure near the whether our data set supports an isotropic layer near the CMB [Tkalcˇic´etal., 2002]. However, the required level of ICB, and show that normal mode data can accommodate an lateral heterogeneity is very high, approximately ±7% over isotropic layer of less than 150 km thickness. However, the bottommost 300 km in the mantle. Although this could be data from body waves penetrating shallowly in the inner an overestimate, it is consistent with the amplitude of core cannot be well fit by a model with an isotropic layer. variations observed using diffracted P waves [Sylvander et In addition, a comparison of BC DF data in the distance al., 1997] and may be related to observations that have been ranges 150 –153 and 153 –155 (using diffracted BC) interpreted as evidence for ULVZs [e.g., Garnero et al., suggests that the topmost inner core is anisotropic. Argu- 1998]. Regions where the ULVZs are observed corresponds ments for an isotropic layer are mainly based upon differ- to regions where we observe very slow velocity anomalies ential travel time data [e.g., Song and Helmberger, 1998; and the ULVZs are not observed where very fast velocity Creager, 1999], however, a weak level of anisotropy can anomalies exist in our residual maps. Good agreement of be accommodated by this data set [e.g., Song and Helm- residual distributions between BC DF and AB DF, in berger, 1995; Creager, 2000; Garcia and Souriau, 2000]. addition to models of P velocity near the CMB, suggests that Recent studies based upon waveform modeling propose much of the residual differential data originates in the mantle inner core models with a 250 km thick isotropic layer in agreement with Breger et al. [1999]. above a highly anisotropic ( 8%) interior [Ouzounis and [42] There are residuals that cannot be entirely explained Creager, 2001; Song and Xu, 2002]. Normal mode obser- by large-wavelength mantle structure near the CMB. The vations would not be consistent with this model since the largest of such anomalies involves observations from path isotropic layer is too thick to fit modes which are only between the South Sandwich Islands and Alaska. The sensitive to the shallow part of the inner core, and the measurements from this path remain anomalous after cor- interior is too strongly anisotropic for modes with deeper rection due to constant anisotropy in the inner core and are sensitivity. In addition, 8% anisotropy overpredicts DF so large that mantle structure alone cannot explain the residual at distances above 150 . In the future, the dif- anomalous values unless there is an enhanced slab effect. fracted BC DF data may be used to constrain anisotropic The observations suggest that there may be small-scale structure near the ICB. In the meantime, one should be variations in the inner core, although the origin of such cautious when using diffracted data for modeling inner core structure within a body that developed under essentially anisotropy: assuming insensitivity to inner core structure homogeneous conditions is unclear. may lead to anisotropic models which are more compli- [43] This study highlights the advantage of combining cated than necessary. different types of data which are sensitive to inner core ESE 21 - 16 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 structure. In particular, normal mode data with less biased Boundary Region, Geodyn. Ser., vol. 28, edited by M. Gurnis et al., pp. 319–334, AGU, Washington, D. C., 1998. sampling of the inner core provide an invaluable constraint Gu, Y. J., A. M. Dziewon´ski, W.-J. Su, and G. 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